X-Git-Url: https://www.ginac.de/ginac.git//ginac.git?p=ginac.git;a=blobdiff_plain;f=ginac%2Fclifford.cpp;h=0a10d4525854f5f575297234aefa33ba0f3fe2db;hp=b8083e8d9e8723c7d7129c872d301703044b12e5;hb=0f617ea4ea1dc6a33cae5e2ce518b26d8055c177;hpb=fbdd5eefb7188778ca9c04b5bee08223609b880f diff --git a/ginac/clifford.cpp b/ginac/clifford.cpp index b8083e8d..0a10d452 100644 --- a/ginac/clifford.cpp +++ b/ginac/clifford.cpp @@ -3,7 +3,7 @@ * Implementation of GiNaC's clifford algebra (Dirac gamma) objects. */ /* - * GiNaC Copyright (C) 1999-2001 Johannes Gutenberg University Mainz, Germany + * GiNaC Copyright (C) 1999-2002 Johannes Gutenberg University Mainz, Germany * * This program is free software; you can redistribute it and/or modify * it under the terms of the GNU General Public License as published by @@ -43,6 +43,8 @@ GINAC_IMPLEMENT_REGISTERED_CLASS(clifford, indexed) GINAC_IMPLEMENT_REGISTERED_CLASS(diracone, tensor) GINAC_IMPLEMENT_REGISTERED_CLASS(diracgamma, tensor) GINAC_IMPLEMENT_REGISTERED_CLASS(diracgamma5, tensor) +GINAC_IMPLEMENT_REGISTERED_CLASS(diracgammaL, tensor) +GINAC_IMPLEMENT_REGISTERED_CLASS(diracgammaR, tensor) ////////// // default ctor, dtor, copy ctor, assignment operator and helpers @@ -63,6 +65,8 @@ DEFAULT_DESTROY(clifford) DEFAULT_CTORS(diracone) DEFAULT_CTORS(diracgamma) DEFAULT_CTORS(diracgamma5) +DEFAULT_CTORS(diracgammaL) +DEFAULT_CTORS(diracgammaR) ////////// // other constructors @@ -116,6 +120,8 @@ DEFAULT_UNARCHIVE(clifford) DEFAULT_ARCHIVING(diracone) DEFAULT_ARCHIVING(diracgamma) DEFAULT_ARCHIVING(diracgamma5) +DEFAULT_ARCHIVING(diracgammaL) +DEFAULT_ARCHIVING(diracgammaR) ////////// // functions overriding virtual functions from base classes @@ -144,7 +150,9 @@ bool clifford::match_same_type(const basic & other) const void clifford::print(const print_context & c, unsigned level) const { - if (!is_a(seq[0]) && !is_a(seq[0]) && !is_a(seq[0])) { + if (!is_a(seq[0]) && !is_a(seq[0]) && + !is_a(seq[0]) && !is_a(seq[0]) && + !is_a(seq[0])) { // dirac_slash() object is printed differently if (is_a(c)) @@ -165,10 +173,14 @@ void clifford::print(const print_context & c, unsigned level) const DEFAULT_COMPARE(diracone) DEFAULT_COMPARE(diracgamma) DEFAULT_COMPARE(diracgamma5) +DEFAULT_COMPARE(diracgammaL) +DEFAULT_COMPARE(diracgammaR) DEFAULT_PRINT_LATEX(diracone, "ONE", "\\mathbb{1}") DEFAULT_PRINT_LATEX(diracgamma, "gamma", "\\gamma") DEFAULT_PRINT_LATEX(diracgamma5, "gamma5", "{\\gamma^5}") +DEFAULT_PRINT_LATEX(diracgammaL, "gammaL", "{\\gamma_L}") +DEFAULT_PRINT_LATEX(diracgammaR, "gammaR", "{\\gamma_R}") /** This function decomposes gamma~mu -> (1, mu) and a\ -> (a.ix, ix) */ static void base_and_index(const ex & c, ex & b, ex & i) @@ -179,6 +191,9 @@ static void base_and_index(const ex & c, ex & b, ex & i) if (is_a(c.op(0))) { // proper dirac gamma object i = c.op(1); b = _ex1; + } else if (is_a(c.op(0)) || is_a(c.op(0)) || is_a(c.op(0))) { // gamma5/L/R + i = _ex0; + b = _ex1; } else { // slash object, generate new dummy index varidx ix((new symbol)->setflag(status_flags::dynallocated), ex_to(c.op(1)).get_dim()); b = indexed(c.op(0), ix.toggle_variance()); @@ -196,6 +211,10 @@ bool diracgamma::contract_with(exvector::iterator self, exvector::iterator other if (is_a(*other)) { + // Contraction only makes sense if the represenation labels are equal + if (ex_to(*other).get_representation_label() != rl) + return false; + ex dim = ex_to(self->op(1)).get_dim(); // gamma~mu gamma.mu = dim ONE @@ -265,7 +284,7 @@ bool diracgamma::contract_with(exvector::iterator self, exvector::iterator other } /** Perform automatic simplification on noncommutative product of clifford - * objects. This removes superfluous ONEs, permutes gamma5's to the front + * objects. This removes superfluous ONEs, permutes gamma5/L/R's to the front * and removes squares of gamma objects. */ ex clifford::simplify_ncmul(const exvector & v) const { @@ -283,17 +302,67 @@ ex clifford::simplify_ncmul(const exvector & v) const bool something_changed = false; int sign = 1; - // Anticommute gamma5's to the front + // Anticommute gamma5/L/R's to the front if (s.size() >= 2) { exvector::iterator first = s.begin(), next_to_last = s.end() - 2; while (true) { exvector::iterator it = next_to_last; while (true) { exvector::iterator it2 = it + 1; - if (is_a(*it) && is_a(*it2) && !is_a(it->op(0)) && is_a(it2->op(0))) { - it->swap(*it2); - sign = -sign; - something_changed = true; + if (is_a(*it) && is_a(*it2)) { + ex e1 = it->op(0), e2 = it2->op(0); + + if (is_a(e2)) { + + if (is_a(e1) || is_a(e1)) { + + // gammaL/R gamma5 -> gamma5 gammaL/R + it->swap(*it2); + something_changed = true; + + } else if (!is_a(e1)) { + + // gamma5 gamma5 -> gamma5 gamma5 (do nothing) + // x gamma5 -> -gamma5 x + it->swap(*it2); + sign = -sign; + something_changed = true; + } + + } else if (is_a(e2)) { + + if (is_a(e1)) { + + // gammaR gammaL -> 0 + return _ex0; + + } else if (!is_a(e1) && !is_a(e1)) { + + // gammaL gammaL -> gammaL gammaL (do nothing) + // gamma5 gammaL -> gamma5 gammaL (do nothing) + // x gammaL -> gammaR x + it->swap(*it2); + *it = clifford(diracgammaR(), ex_to(*it).get_representation_label()); + something_changed = true; + } + + } else if (is_a(e2)) { + + if (is_a(e1)) { + + // gammaL gammaR -> 0 + return _ex0; + + } else if (!is_a(e1) && !is_a(e1)) { + + // gammaR gammaR -> gammaR gammaR (do nothing) + // gamma5 gammaR -> gamma5 gammaR (do nothing) + // x gammaR -> gammaL x + it->swap(*it2); + *it = clifford(diracgammaL(), ex_to(*it).get_representation_label()); + something_changed = true; + } + } } if (it == first) break; @@ -305,12 +374,6 @@ ex clifford::simplify_ncmul(const exvector & v) const } } - // Remove squares of gamma5 - while (s.size() >= 2 && is_a(s[0]) && is_a(s[1]) && is_a(s[0].op(0)) && is_a(s[1].op(0))) { - s.erase(s.begin(), s.begin() + 2); - something_changed = true; - } - // Remove equal adjacent gammas if (s.size() >= 2) { exvector::iterator it, itend = s.end() - 1; @@ -319,7 +382,14 @@ ex clifford::simplify_ncmul(const exvector & v) const ex & b = it[1]; if (!is_a(a) || !is_a(b)) continue; - if (is_a(a.op(0)) && is_a(b.op(0))) { + + const ex & ag = a.op(0); + const ex & bg = b.op(0); + bool a_is_diracgamma = is_a(ag); + bool b_is_diracgamma = is_a(bg); + + if (a_is_diracgamma && b_is_diracgamma) { + const ex & ia = a.op(1); const ex & ib = b.op(1); if (ia.is_equal(ib)) { // gamma~alpha gamma~alpha -> g~alpha~alpha @@ -327,15 +397,46 @@ ex clifford::simplify_ncmul(const exvector & v) const b = dirac_ONE(representation_label); something_changed = true; } - } else if (!is_a(a.op(0)) && !is_a(b.op(0))) { - const ex & ba = a.op(0); - const ex & bb = b.op(0); - if (ba.is_equal(bb)) { // a\ a\ -> a^2 - varidx ix((new symbol)->setflag(status_flags::dynallocated), ex_to(a.op(1)).get_dim()); - a = indexed(ba, ix) * indexed(bb, ix.toggle_variance()); - b = dirac_ONE(representation_label); - something_changed = true; - } + + } else if ((is_a(ag) && is_a(bg))) { + + // Remove squares of gamma5 + a = dirac_ONE(representation_label); + b = dirac_ONE(representation_label); + something_changed = true; + + } else if ((is_a(ag) && is_a(bg)) + || (is_a(ag) && is_a(bg))) { + + // Remove squares of gammaL/R + b = dirac_ONE(representation_label); + something_changed = true; + + } else if (is_a(ag) && is_a(bg)) { + + // gammaL and gammaR are orthogonal + return _ex0; + + } else if (is_a(ag) && is_a(bg)) { + + // gamma5 gammaL -> -gammaL + a = dirac_ONE(representation_label); + sign = -sign; + something_changed = true; + + } else if (is_a(ag) && is_a(bg)) { + + // gamma5 gammaR -> gammaR + a = dirac_ONE(representation_label); + something_changed = true; + + } else if (!a_is_diracgamma && !b_is_diracgamma && ag.is_equal(bg)) { + + // a\ a\ -> a^2 + varidx ix((new symbol)->setflag(status_flags::dynallocated), ex_to(a.op(1)).get_dim()); + a = indexed(ag, ix) * indexed(ag, ix.toggle_variance()); + b = dirac_ONE(representation_label); + something_changed = true; } } } @@ -380,6 +481,16 @@ ex dirac_gamma5(unsigned char rl) return clifford(diracgamma5(), rl); } +ex dirac_gammaL(unsigned char rl) +{ + return clifford(diracgammaL(), rl); +} + +ex dirac_gammaR(unsigned char rl) +{ + return clifford(diracgammaR(), rl); +} + ex dirac_gamma6(unsigned char rl) { return clifford(diracone(), rl) + clifford(diracgamma5(), rl); @@ -452,9 +563,13 @@ ex dirac_trace(const ex & e, unsigned char rl, const ex & trONE) { if (is_a(e)) { - if (ex_to(e).get_representation_label() == rl - && is_a(e.op(0))) + if (!ex_to(e).get_representation_label() == rl) + return _ex0; + const ex & g = e.op(0); + if (is_a(g)) return trONE; + else if (is_a(g) || is_a(g)) + return trONE/2; else return _ex0; @@ -476,8 +591,11 @@ ex dirac_trace(const ex & e, unsigned char rl, const ex & trONE) if (!is_clifford_tinfo(e.return_type_tinfo(), rl)) return _ex0; - // Expand product, if necessary - ex e_expanded = e.expand(); + // Substitute gammaL/R and expand product, if necessary + ex e_expanded = e.subs(lst( + dirac_gammaL(rl) == (dirac_ONE(rl)-dirac_gamma5(rl))/2, + dirac_gammaR(rl) == (dirac_ONE(rl)+dirac_gamma5(rl))/2 + )).expand(); if (!is_a(e_expanded)) return dirac_trace(e_expanded, rl, trONE); @@ -493,17 +611,19 @@ ex dirac_trace(const ex & e, unsigned char rl, const ex & trONE) return _ex0; // Tr gamma5 gamma.mu gamma.nu gamma.rho gamma.sigma = 4I * epsilon(mu, nu, rho, sigma) + // (the epsilon is always 4-dimensional) if (num == 5) { ex b1, i1, b2, i2, b3, i3, b4, i4; base_and_index(e.op(1), b1, i1); base_and_index(e.op(2), b2, i2); base_and_index(e.op(3), b3, i3); base_and_index(e.op(4), b4, i4); - return trONE * I * (eps0123(i1, i2, i3, i4) * b1 * b2 * b3 * b4).simplify_indexed(); + return trONE * I * (lorentz_eps(ex_to(i1).replace_dim(_ex4), ex_to(i2).replace_dim(_ex4), ex_to(i3).replace_dim(_ex4), ex_to(i4).replace_dim(_ex4)) * b1 * b2 * b3 * b4).simplify_indexed(); } // Tr gamma5 S_2k = // I/4! * epsilon0123.mu1.mu2.mu3.mu4 * Tr gamma.mu1 gamma.mu2 gamma.mu3 gamma.mu4 S_2k + // (the epsilon is always 4-dimensional) exvector ix(num-1), bv(num-1); for (unsigned i=1; i(idx1).replace_dim(_ex4), ex_to(idx2).replace_dim(_ex4), ex_to(idx3).replace_dim(_ex4), ex_to(idx4).replace_dim(_ex4)) * trace_string(v.begin(), num - 4); } }